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Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions

By Alin Bostan, Frédéric Chyzak, Pierre Lairez and Bruno Salvy

Abstract

International audienceHermite reduction is a classical algorithmic tool in symbolic integration. It is used to decompose a given rational function as a sum of a function with simple poles and the derivative of another rational function. We extend Hermite reduction to arbitrary linear differential operators instead of the pure derivative, and develop efficient algorithms for this reduction. We then apply the generalized Hermite reduction to the computation of linear operators satisfied by single definite integrals of D-finite functions of several continuous or discrete parameters. The resulting algorithm is a generalization of reduction-based methods for creative telescoping

Topics: ACM: I.: Computing Methodologies/I.1: SYMBOLIC AND ALGEBRAIC MANIPULATION/I.1.2: Algorithms, [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC]
Publisher: 'Association for Computing Machinery (ACM)'
Year: 2018
DOI identifier: 10.1145/3208976.3208992
OAI identifier: oai:HAL:hal-01788619v1
Provided by: HAL-ENS-LYON
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